In safety-critical domains such as autonomous driving and medical diagnosis, the reliability of machine learning models is crucial. One significant challenge to reliability is concept drift, which can cause model deterioration over time. Traditionally, drift detectors rely on true labels, which are often scarce and costly. This study conducts a comprehensive empirical evaluation of using uncertainty values as substitutes for error rates in detecting drifts, aiming to alleviate the reliance on labeled post-deployment data. We examine five uncertainty estimation methods in conjunction with the ADWIN detector across seven real-world datasets. Our results reveal that while the SWAG method exhibits superior calibration, the overall accuracy in detecting drifts is not notably impacted by the choice of uncertainty estimation method, with even the most basic method demonstrating competitive performance. These findings offer valuable insights into the practical applicability of uncertainty-based drift detection in real-world, safety-critical applications.